Another vote here for the Oakley M-Frame. They've been my dad's go-to favorite anything outdoors for decades now. I used them for a long time as well until I switched to the Oakley Fives-squared, but that was only because they fit better in a motorcycle helmet. A bicycle helmet doesn't enclose the face on the sides so the sections near the temples where they stick out a bit isn't an issue when biking.
My dad has been in a similar boat as the OP for the entire time I've been alive, that is he can see fine when doing daily activities but needs reading glasses for up close. So, he just carries reading glasses for when he needs them. When on the bike, he can manage without so he leaves them at home.
They're available in both folding and non-folding frames. The rubber on the sides and nose piece prevent it from sliding around. They wrap around pretty far and don't distort near the edges. Lenses are easy to swap and many different colors and shades are made, polarized and non-polarized. I find moderately dark polarized works just fine for me. The polarizing does obscure a small corner on my cycling computer but nothing I pay much mind to, it's not a GPS so all I'm missing out on is the tenths of a MPH for my speed and I can even kind of read that.
This is all, of course, if you're not someone who tends to lose or break their glasses. Oakley's are not cheap.